If everyone has free healthcare, then it will take a while to get the healthcare because it will always be full of sick people. People will have to wait for cancer treatment when they only have a month to live.
There is some truth to what to you said but some people who don't need any healthcare and are in healthy shape are paying for something that they don't even know. Even if we are paying higher taxes, the people who are not even needing the healthcare are still paying for someone else's healthcare. It doesn't seem right in my opinion. I like to spend the money on my self not others.